Re: New experimental GP interface for elliptic curves over finite fields

[Bill Allombert <Bill.Allombert@math.u-bordeaux1.fr>]

On Thu, Jul 26, 2012 at 08:33:37PM +0200, Bill Allombert wrote:
> On Thu, Jul 12, 2012 at 07:47:37PM +0200, Bill Allombert wrote:
> > On Thu, Jun 07, 2012 at 12:16:11PM +0200, Bill Allombert wrote:
> > > Dear PARI developers,
> > > 
> > > I have added a new experimental interface for elliptic curves over finite
> > > fields.
> > > A new function ellffinit is provided to create curves over finite fields:
> > > 
> > > Create a curves over F_7:
> > > ? E=ellffinit([1,3],7);
> > > 
> > > Create a curves over F_101^3:
> > > ? a=ffgen(ffinit(101,3),'a);
> > > ? E=ellffinit([1,a^3],a);
> > > 
> > > (for technical reasons, the characteristic must be >3. This will be fixed eventually.)
> > 
> > I have just added support for ordinary curves over finite field of characteristic 2.
> 
> I have added support for supersingular curves over finite field of characteristic 2,
> and corrected a lot of bugs.

I have reimplemented the support for ordinary curves over finite field of characteristic 2
to use Harley algorithm. This is much faster now.

? a=ffgen(ffinit(2,1024),'a);ellffinit([1,0,0,0,a],a,1);
? ##
  ***   last result computed in 11,482 ms.

(I like the ellffinit interface less and less. Indeed, why wasting time computing
the group structure if you are looking for curves of prime order ?)

Cheers,
Bill.